g(x)=sqrt (4x+1) and g(x)=5 a Solve the equation g(x)=5 b State the domain and range of the function.

Question

Answer 1

a) To solve the equation

, we need to find the value of

for which

.Given that

, we can substitute this into the equation:

To solve for

, we can square both sides of the equation:

Therefore, the solution to the equation

is

.b) To state the domain and range of the function

, we need to consider the restrictions on the input values (domain) and the possible output values (range).Domain:The domain of the function

is the set of all real numbers

for which the expression under the square root is non-negative. In other words, the domain is the set of all

such that

.Solving the inequality

, we get:

Therefore, the domain of the function

is

.Range:The range of the function

is the set of all possible output values. Since the square root function always produces non-negative values, the range of the function is

.In summary:a) The solution to the equation

is

.b) The domain of the function

is

, and the range is

.

Soru